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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 101430fc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.ew2 | 101430fc1 | \([1, -1, 1, -711122, 230986221]\) | \(463702796512201/15214500\) | \(1304888647954500\) | \([2]\) | \(1105920\) | \(1.9941\) | \(\Gamma_0(N)\)-optimal |
| 101430.ew3 | 101430fc2 | \([1, -1, 1, -680252, 251928429]\) | \(-405897921250921/84358968750\) | \(-7235141521247718750\) | \([2]\) | \(2211840\) | \(2.3407\) | |
| 101430.ew1 | 101430fc3 | \([1, -1, 1, -1273397, -181578099]\) | \(2662558086295801/1374177967680\) | \(117857913851576969280\) | \([2]\) | \(3317760\) | \(2.5434\) | |
| 101430.ew4 | 101430fc4 | \([1, -1, 1, 4777123, -1413463971]\) | \(140574743422291079/91397357868600\) | \(-7838796854038649700600\) | \([2]\) | \(6635520\) | \(2.8900\) |
Rank
sage: E.rank()
The elliptic curves in class 101430fc have rank \(0\).
Complex multiplication
The elliptic curves in class 101430fc do not have complex multiplication.Modular form 101430.2.a.fc
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
